IEEE Transactions on Information Theory最新文献

{"title":"Byzantine-Resilient Gradient Coding Through Local Gradient Computations","authors":"Christoph Hofmeister;Luis Maßny;Eitan Yaakobi;Rawad Bitar","doi":"10.1109/TIT.2025.3542896","DOIUrl":"https://doi.org/10.1109/TIT.2025.3542896","url":null,"abstract":"We consider gradient coding in the presence of an adversary controlling so-called malicious workers trying to corrupt the computations. Previous works propose the use of MDS codes to treat the responses from malicious workers as errors and correct them using the error-correction properties of the code. This comes at the expense of increasing the replication, i.e., the number of workers <italic>each partial gradient</i> is computed by. In this work, we propose a way to reduce the replication to <inline-formula> <tex-math>$ {s} +1$ </tex-math></inline-formula> instead of <inline-formula> <tex-math>$2 {s} +1$ </tex-math></inline-formula> in the presence of <italic>s</i> malicious workers. Our method detects erroneous inputs from the malicious workers, transforming them into erasures. This comes at the expense of <italic>s</i> additional local computations at the main node and additional rounds of light communication between the main node and the workers. We define a general framework and give fundamental limits for fractional repetition data allocations. Our scheme is optimal in terms of replication and local computation and incurs a communication cost that is asymptotically, in the size of the dataset, a multiplicative factor away from the derived bound. We furthermore show how additional redundancy can be exploited to reduce the number of local computations and communication cost, or, alternatively, tolerate straggling workers.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"3142-3156"},"PeriodicalIF":2.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10891921","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143667312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum Ruzsa Divergence to Quantify Magic","authors":"Kaifeng Bu;Weichen Gu;Arthur Jaffe","doi":"10.1109/TIT.2025.3543276","DOIUrl":"https://doi.org/10.1109/TIT.2025.3543276","url":null,"abstract":"In this work, we investigate the behavior of quantum entropy under quantum convolution and its application in quantifying magic. We first establish an entropic, quantum central limit theorem (q-CLT), where the rate of convergence is bounded by the magic gap. We also introduce a new quantum divergence based on quantum convolution, called the quantum Ruzsa divergence, to study the stabilizer structure of quantum states. We conjecture a “convolutional strong subadditivity” inequality, which leads to the triangle inequality for the quantum Ruzsa divergence. In addition, we propose two new magic measures, the quantum Ruzsa divergence of magic and quantum-doubling constant, to quantify the amount of magic in quantum states. Finally, by using the quantum convolution, we extend the classical, inverse sumset theory to the quantum case. These results shed new insight into the study of the stabilizer and magic states in quantum information theory.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2726-2740"},"PeriodicalIF":2.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Constructing (h, d) Cooperative MSR Codes With Sub-Packetization (d − k + h)(d − k + 1)⌈n/2⌉","authors":"Zihao Zhang;Guodong Li;Sihuang Hu","doi":"10.1109/TIT.2025.3542118","DOIUrl":"https://doi.org/10.1109/TIT.2025.3542118","url":null,"abstract":"We address the multi-node failure repair challenges for MDS array codes. Presently, two primary models are employed for multi-node repairs: the centralized model where all failed nodes are restored in a singular data center, and the cooperative model where failed nodes acquire data from auxiliary nodes and collaborate amongst themselves for the repair process. This paper focuses on the cooperative model, and we provide explicit constructions of optimal MDS array codes with <italic>d</i> helper nodes under this model. The sub-packetization level of our new codes is <inline-formula> <tex-math>$(d-k+h)(d-k+1)^{lceil n/2 rceil }$ </tex-math></inline-formula> where <italic>h</i> is the number of failed nodes, <italic>k</i> the number of information nodes, and <italic>n</i> the code length. This improves upon recent constructions by Liu et al. (IEEE Transactions on Information Theory, Vol. 69, 2023).","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2505-2516"},"PeriodicalIF":2.2,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fundamental Limits of Covert Communication Over Classical-Quantum Channels","authors":"Michael S. Bullock;Azadeh Sheikholeslami;Mehrdad Tahmasbi;Robert C. Macdonald;Saikat Guha;Boulat A. Bash","doi":"10.1109/TIT.2025.3537970","DOIUrl":"https://doi.org/10.1109/TIT.2025.3537970","url":null,"abstract":"We investigate covert communication over general memoryless classical-quantum channels with fixed finite-size input alphabets. We show that the square root law (SRL) governs covert communication in this setting when product a of <italic>n</i> input states is used: <inline-formula> <tex-math>$L_{mathrm { SRL}}sqrt {n}+o(sqrt {n})$ </tex-math></inline-formula> covert bits (but no more) can be reliably transmitted in <italic>n</i> uses of classical-quantum channel, where <inline-formula> <tex-math>$L_{mathrm { SRL}}gt 0$ </tex-math></inline-formula> is a channel-dependent constant that we call <italic>covert capacity</i>. We also show that ensuring covertness requires <inline-formula> <tex-math>$J_{mathrm { SRL}}sqrt {n}+o(sqrt {n})$ </tex-math></inline-formula> bits secret key shared by the communicating parties prior to transmission, where <inline-formula> <tex-math>$J_{mathrm { SRL}}geq 0$ </tex-math></inline-formula> is a channel-dependent constant. We assume a quantum-powerful adversary that can perform an arbitrary joint (entangling) measurement on all <italic>n</i> channel uses. We determine the single-letter expressions for <inline-formula> <tex-math>$L_{mathrm { SRL}}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$J_{mathrm { SRL}}$ </tex-math></inline-formula>, and establish conditions when <inline-formula> <tex-math>$J_{mathrm { SRL}}=0$ </tex-math></inline-formula> (i.e., no pre-shared secret key is needed). Finally, we evaluate scenarios where covert communication is not governed by the SRL.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2741-2762"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Comprehensive Study on Ziv-Zakai Lower Bounds on the MMSE","authors":"Minoh Jeong;Alex Dytso;Martina Cardone","doi":"10.1109/TIT.2025.3541987","DOIUrl":"https://doi.org/10.1109/TIT.2025.3541987","url":null,"abstract":"This paper explores Bayesian lower bounds on the minimum mean squared error (MMSE) that belong to the well-known Ziv-Zakai family. The Ziv-Zakai technique relies on connecting the bound to an <inline-formula> <tex-math>$mathsf M$ </tex-math></inline-formula>-ary hypothesis testing problem. There are three versions of the Ziv-Zakai bound (ZZB): the first version relies on the so-called <italic>valley-filling function</i>, the second one is a relaxation of the first bound which omits the valley-filling function, and the third one, namely the single-point ZZB (SZZB), replaces the integration present in the first two bounds with a single point maximization. The first part of this paper focuses on providing the most general version of the bounds. It is shown that these bounds hold without any assumption on the distribution of the estimand. This makes the bounds applicable to discrete and mixed distributions. Then, the SZZB is extended to an <inline-formula> <tex-math>$mathsf M$ </tex-math></inline-formula>-ary setting and a version of it that holds for the multivariate setting is provided. In the second part, general properties of these bounds are provided. First, unlike the Bayesian <italic>Cramér-Rao bound</i>, it is shown that all the versions of the ZZB <italic>tensorize</i>. Second, a characterization of the <italic>high-noise</i> asymptotic is provided, which is used to argue about the tightness of the bounds. Third, a complete <italic>low-noise</i> asymptotic is provided under the assumptions of mixed-input distributions and Gaussian additive noise channels. In the low-noise, it is shown that the ZZB is generally tight, but there are examples for which the SZZB is not tight. In the third part, the tightness of the bounds is evaluated. First, it is shown that in the low-noise regime the ZZB without the valley-filling function, and, therefore, also the ZZB with the valley-filling function, are tight for mixed-input distributions and Gaussian additive noise channels. Second, for discrete inputs it is shown that the ZZB with the valley-filling function is always sub-optimal, and equal to zero without the valley-filling function. Third, unlike for the ZZB, an example is shown for which the SZZB is tight to the MMSE for discrete inputs. Fourth, sufficient and necessary conditions for the tightness of the bounds are provided. Finally, some examples are provided in which the bounds in the Ziv-Zakai family outperform other well-known Bayesian lower bounds, namely the Cramér-Rao bound and the maximum entropy bound.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"3214-3236"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143667259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Blind Interference Alignment for MapReduce: Exploiting Side-Information With Reconfigurable Antennas","authors":"Yuxiang Lu;Syed A. Jafar","doi":"10.1109/TIT.2025.3541808","DOIUrl":"https://doi.org/10.1109/TIT.2025.3541808","url":null,"abstract":"In order to explore how blind interference alignment (BIA) schemes may take advantage of side-information in computation tasks, we study the degrees of freedom (DoF) of a <italic>K</i> user wireless network setting that arises in full-duplex wireless MapReduce applications. In this setting the receivers are assumed to have reconfigurable antennas and channel knowledge, while the transmitters have neither, i.e., the transmitters lack channel knowledge and are only equipped with conventional antennas. The central ingredient of the problem formulation is the message structure arising out of the Shuffle phase of MapReduce, whereby each transmitter has a subset of messages that need to be delivered to various receivers, and each receiver has a subset of messages available to it in advance as side-information. We approach this problem by decomposing it into distinctive stages that help identify key ingredients of the overall solution. The novel elements that emerge from the first stage, called broadcast with groupcast messages, include an outer maximum distance separable (MDS) code structure at the transmitter, and an algorithm for iteratively determining groupcast-optimal reconfigurable antenna switching patterns at the receiver to achieve intra-message (among the symbols of the same message) alignment. The next stage, called unicast with side-information, reveals optimal inter-message (among symbols of different messages) alignment patterns to exploit side-information, and by a relabeling of messages, connects to the desired MapReduce setting.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2604-2625"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"MDS Variable Generation and Secure Summation With User Selection","authors":"Yizhou Zhao;Hua Sun","doi":"10.1109/TIT.2025.3541551","DOIUrl":"https://doi.org/10.1109/TIT.2025.3541551","url":null,"abstract":"A collection of <italic>K</i> random variables are called <inline-formula> <tex-math>$(K,n)$ </tex-math></inline-formula>-MDS if any <italic>n</i> of the <italic>K</i> variables are independent and determine all remaining variables. In the MDS variable generation problem, <italic>K</i> users wish to generate variables that are <inline-formula> <tex-math>$(K,n)$ </tex-math></inline-formula>-MDS using a randomness variable owned by each user. We show that to generate 1 bit of <inline-formula> <tex-math>$(K,n)$ </tex-math></inline-formula>-MDS variables for each <inline-formula> <tex-math>$n in {1,2,cdots , K}$ </tex-math></inline-formula>, the minimum size of the randomness variable at each user is <inline-formula> <tex-math>$1 + 1/2 + cdots + 1/K$ </tex-math></inline-formula> bits. An intimately related problem is secure summation with user selection, where a server may select an arbitrary subset of <italic>K</i> users and securely compute the sum of the inputs of the selected users. We show that to compute 1 bit of an arbitrarily chosen sum securely, the minimum size of the key held by each user is <inline-formula> <tex-math>$1 + 1/2 + cdots + 1/(K-1)$ </tex-math></inline-formula> bits, whose achievability uses the generation of <inline-formula> <tex-math>$(K,n)$ </tex-math></inline-formula>-MDS variables for <inline-formula> <tex-math>$n in {1,2,cdots ,K-1}$ </tex-math></inline-formula>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"3129-3141"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143667375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On k-Mer-Based and Maximum Likelihood Estimation Algorithms for Trace Reconstruction","authors":"Kuan Cheng;Elena Grigorescu;Xin Li;Madhu Sudan;Minshen Zhu","doi":"10.1109/TIT.2025.3541375","DOIUrl":"https://doi.org/10.1109/TIT.2025.3541375","url":null,"abstract":"The goal of the trace reconstruction problem is to recover a string &lt;inline-formula&gt; &lt;tex-math&gt;$mathbf {x}in {0,1}^{n}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; given many independent &lt;italic&gt;traces&lt;/i&gt; of &lt;bold&gt;x&lt;/b&gt;, where a trace is a subsequence obtained from deleting bits of &lt;bold&gt;x&lt;/b&gt; independently with some given probability &lt;inline-formula&gt; &lt;tex-math&gt;$pin [0,1$ &lt;/tex-math&gt;&lt;/inline-formula&gt;). A recent result of Chase (STOC 2021) shows how &lt;bold&gt;x&lt;/b&gt; can be determined (in exponential time) from &lt;inline-formula&gt; &lt;tex-math&gt;$exp ({O}(n^{1/5})log ^{5} n)$ &lt;/tex-math&gt;&lt;/inline-formula&gt; traces. This is the state-of-the-art result on the sample complexity of trace reconstruction. In this paper we consider two kinds of algorithms for the trace reconstruction problem. We first observe that the bound of Chase, which is based on statistics of arbitrary length-&lt;italic&gt;k&lt;/i&gt; subsequences, can also be obtained by considering the “&lt;italic&gt;k&lt;/i&gt;-mer statistics”, i.e., statistics regarding occurrences of &lt;italic&gt;contiguous k&lt;/i&gt;-bit strings (a.k.a, &lt;italic&gt;k-mers&lt;/i&gt;) in the initial string &lt;bold&gt;x&lt;/b&gt;, for &lt;inline-formula&gt; &lt;tex-math&gt;$k = 2n^{1/5}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. Mazooji and Shomorony (arXiv.2210.10917) show that such statistics (called &lt;italic&gt;k&lt;/i&gt;-mer density map) can be estimated within &lt;inline-formula&gt; &lt;tex-math&gt;$varepsilon $ &lt;/tex-math&gt;&lt;/inline-formula&gt; accuracy from &lt;inline-formula&gt; &lt;tex-math&gt;$ {mathrm {poly}} (n, 2^{k}, 1/ {varepsilon })$ &lt;/tex-math&gt;&lt;/inline-formula&gt; traces. We call an algorithm to be &lt;italic&gt;k-mer-based&lt;/i&gt; if it reconstructs &lt;bold&gt;x&lt;/b&gt; given estimates of the &lt;italic&gt;k&lt;/i&gt;-mer density map. Such algorithms essentially capture all the analyses in the worst-case and smoothed-complexity models of the trace reconstruction problem we know of so far. Our first, and technically more involved, result shows that any &lt;italic&gt;k&lt;/i&gt;-mer-based algorithm for trace reconstruction must use &lt;inline-formula&gt; &lt;tex-math&gt;$exp (Omega (n^{1/5} sqrt {log n}))$ &lt;/tex-math&gt;&lt;/inline-formula&gt; traces, thus establishing the optimality of this number of traces. The analysis of this result also shows that the analysis technique used by Chase (STOC 2021) is essentially tight, and hence new techniques are needed in order to improve the worst-case upper bound. This result is shown by considering an appropriate class of real polynomials, that have been previously studied in the context of trace estimation (De, O’Donnell, Servedio. Annals of Probability 2019; Nazarov, Peres. STOC 2017), and proving that two of these polynomials are very close to each other on an arc in the complex plane. Our proof of the proximity of such polynomials uses new technical ingredients that allow us to focus on just a few coefficients of these polynomials. Our second, simple, result considers the performance of the Maximum Likelihood Estimator (MLE), which specifically picks the source string that has the maximum likelihood to generate the samples (traces). We show that the MLE algorith","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2591-2603"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New Bounds for Generalized Column Distances and Construction of Convolutional Codes","authors":"Xu Pan;Hao Chen;Chunming Tang;Xueyan Chen","doi":"10.1109/TIT.2025.3539914","DOIUrl":"https://doi.org/10.1109/TIT.2025.3539914","url":null,"abstract":"Based on known bounds for relative generalized Hamming weights of linear codes, we provide several new bounds for generalized column distances of convolutional codes, including the Griesmer-type bound for generalized column distances. Then we construct several infinite families of convolutional codes such that the (1, 1)-Griesmer defect of these convolutional codes is small compared with the length of these convolutional codes by using cyclic codes, negacyclic codes and GRS codes. In particular, we obtain some convolutional codes such that the (1, 1)-Griesmer defect of these convolutional codes is zero or one. Next we prove that the 2-generalized column distance sequence <inline-formula> <tex-math>${d_{2,j}(mathcal {C})}_{j=1}^{infty }$ </tex-math></inline-formula> of any convolutional code <inline-formula> <tex-math>$mathcal {C}$ </tex-math></inline-formula> is increasing and bounded from above, and the limit of the sequence <inline-formula> <tex-math>${d_{2,j}(mathcal {C})}_{j=1}^{infty }$ </tex-math></inline-formula> is related to the 2-generalized Hamming weight of the convolutional code <inline-formula> <tex-math>$mathcal {C}$ </tex-math></inline-formula>. For <inline-formula> <tex-math>$ige 3$ </tex-math></inline-formula>, we prove that the <italic>i</i>-generalized column distance sequence <inline-formula> <tex-math>${d_{i,j}(mathcal {C})}_{j=lceil frac {i}{k}-1rceil }^{infty }$ </tex-math></inline-formula> of any convolutional code <inline-formula> <tex-math>$mathcal {C}$ </tex-math></inline-formula> is bounded above and below.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2576-2590"},"PeriodicalIF":2.2,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Distributed Quantum Faithful Simulation and Function Computation Using Algebraic Structured Measurements","authors":"Touheed Anwar Atif;S. Sandeep Pradhan","doi":"10.1109/TIT.2025.3539082","DOIUrl":"https://doi.org/10.1109/TIT.2025.3539082","url":null,"abstract":"We consider the task of faithfully simulating a quantum measurement, acting on a joint bipartite quantum state, in a distributed manner. In this setup, the constituent sub-systems of the joint quantum state are measured by two agents, Alice and Bob. A third agent, Charlie, receives the measurement outcomes sent by Alice and Bob. Charlie uses local and pairwise shared randomness to compute a bivariate function of the measurement outcomes. The objective of three agents is to faithfully simulate the given distributed quantum measurement acting on the given quantum state while minimizing the communication and shared randomness rates. We demonstrate a new inner bound to the rate region using random structured POVMs based on asymptotically good algebraic codes, and characterize the performance limit using single-letter quantum mutual information quantities. This new bound subsumes the largest known inner bound and improves upon it strictly for identified examples. One of the challenges in analyzing these structured POVMs is that they exhibit only pairwise independence and induce only uniform single-letter distributions. We address these in the non-commutative quantum setting, and provide a two-party distributed faithful simulation and function computation protocol.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2800-2825"},"PeriodicalIF":2.2,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143667373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}